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Question

The area enclosed by the curve y=4x2,y2sin(xπ22) and the x-axis divided by the y - axis in the ratio

A
π28π2+8
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B
π24π2+4
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C
π4π+4
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D
2π22π+π28
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Solution

The correct option is D 2π22π+π28
y=4x2,y=2sin(xπ22)
intersect at x=2
Area to the left of y-axis is π
Area to the right of y-axis
=20(4x22sinxπ22)dx
=(x4x22+42sin1x2)20+(4πcosxπ22)20
=(1+2×π4)+π4(01)=1+π24π
=2π+π282π sq. units

Ratio=2π22π+π28

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